Does the Alternating Series Converge Conditionally?

[rcmango]

Homework Statement

heres the equation that will converge conditionally: http://img440.imageshack.us/img440/9945/untitled3jg.jpg

changes to
An = n/(1 + nLNn)

Homework Equations

alternating series equation.
converges conditionally.

d/dn An = (1-n)/(1+nLNn)^2

The Attempt at a Solution

I'm not sure how the first equation changes to the second equation, and then I'm supposed to use l'hospital's rule.

any help please.

 

[cristo]

Is the equation in the picture meant to read $$\sum_{n=2}^{\infty}\frac{(-1)^nn}{1+nlNn}$$?

Try to learn LaTex; it's very easy to use. Click on the equation to see the code. The tutorial is here: https://www.physicsforums.com/showthread.php?t=8997

 

[Gib Z]

An alternating series converges if it meets two conditions: The last term converges to zero and the terms, ignoring the signs, are non-increasing.

The 1st one is met easily. for the 2nd check check the derivative, if its negative for positive infinity, then it converges.